The study is based on the hypothesis that HIVIG will decrease viral burdens in children with moderately advanced HIV infection. Its primary objectives include evaluating HIVIG's (a) safety & tolerance; (b) dosage & pharmacokinetics by serial measurements of immunoglobulins, anti-p24 antibody & rubella antibody titers, and (c) anti-viral activity at 3 dosage levels by assays of viral burden. Its secondary goal will be to collect lab & clinical data by monitoring growth/weight, CD4 counts, incidence of opportun. infections, & survival rates.